Question

if the sum of squares of a polynomial is f(x) =x^2-8x+k is 40 then find the value of k

Answer 1

Heya !!!



P(X) = X² - 8X + K




Here,



A = 1 , B = -8 and C = K




Sum of zeroes = -B/A



Alpha + Beta = -(-8)/1




Alpha + Beta = 8




And,



Product of zeroes = C/A



Alpha × Beta = K -----(2)




According to question,



( Alpha²) + ( Beta)²= 40




( Alpha + Beta)² - 2Alpha Beta = 40



(8)² - 2 × K = 40




64 - 2K = 40



-2K = 40 - 64



-2K = -24



K = 24/2



K = 12




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